In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of …

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions.. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear …

converges towards the standard normal distribution (,).. Multidimensional CLT. Proofs that use characteristic functions can be extended to cases where each individual is a random vector in , with mean vector = [] and covariance matrix (among the components of the vector), and these random vectors are independent and identically distributed. Summation of these vectors is …

The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. If the random variable is denoted by , then it is also known as the expected value of (denoted ()).For a discrete probability distribution, the mean is given by (), where the sum is taken over all possible values of the random variable and () is the probability …

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems.

In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. Although some believe that Generalized estimating equations are robust in everything even with the wrong choice of working-correlation matrix, Generalized estimating …

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of …

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In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.Variance has a central role in statistics, where some ideas that use it include descriptive …

In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if and are -times differentiable functions, then the product is also -times differentiable and its th derivative is given by () = = () (),where () =!! ()! is the binomial coefficient and () denotes the jth derivative of f (and in ...